Estimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor

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1 Glyndŵr University Reserch Online Conference Presenttion Estimtion of the prticle concentrtion in hydrulic liquid by the in-line utomtic prticle counter bsed on the CMOS imge sensor Kornilin, D.V., Kudryvtsev, I.A., McMilln, A.J., Osnlou, A. nd Rtcliffe, I. This is the text of pper presented t Opticl Mesurement Systems for Industril Inspection X, 5 June 917, Munich, Germny. The definitive version of this pper is vilble t: Recommended cittion: Kornilin, D.V., Kudryvtsev, I.A., McMilln, A.J., Osnlou, A. nd Rtcliffe, I. (017), Estimtion of the prticle concentrtion in hydrulic liquid by the in-line utomtic prticle counter bsed on the CMOS imge sensor, Proc. SPIE 1039, Opticl Mesurement Systems for Industril Inspection X, 10394K (June 6, 017); doi: /1.7059

2 Estimtion of the prticle concentrtion in hydrulic liquid by the inline utomtic prticle counter bsed on the CMOS imge sensor Dmitriy V. Kornilin *,b, Ily A. Kudryvtsev, Alison J. McMilln b, Ardeshir Osnlou b, In Rtcliffe b Smr Ntionl Reserch University, 34 Moskovskoe Shosse, Smr, Russi, ; b Glyndwr University, Mold Rod, Wrexhm, Wles, UK, LL11 AW ABSTRACT Modern hydrulic systems should be monitored on the regulr bsis. One of the most effective wys to ddress this tsk is utilizing in-line utomtic prticle counters (APC) built inside of the system. The mesurement of prticle concentrtion in hydrulic liquid by APC is crucil becuse incresing numbers of prticles should men functionl problems. Existing utomtic prticle counters hve significnt limittion for the precise mesurement of reltively low concentrtion of prticle in erospce systems or they re unble to mesure higher concentrtion in industril ones. Both issues cn be ddressed by implementtion of the CMOS imge sensor insted of single photodiode used in the most of APC. CMOS imge sensor helps to overcome the problem of the errors in volume mesurement cused by inequlity of prticle speed inside of tube. Correction is bsed on the determintion of the prticle position nd prbolic velocity distribution profile. Proposed lgorithms re lso suitble for reducing the errors relted to the prticles mtches in mesurement volume. The results of simultion show tht the ccurcy incresed up to 90 per cent nd the resolution improved ten times more compred to the single photodiode sensor. Keywords: CMOS mtrix sensor, imge processing, utomtic prticles counters, hydrulic systems, dignostic, concentrtion mesurement 1. INTRODUCTION The relibility of hydrulic systems depends on the regulr monitoring of their stte 1. One of the most effective wys to ddress this tsk is utilizing in-line utomtic prticle counters (APC) built inside of the system in order to get informtion bout wering processes inside of it, 3, 4. The informtion bout the stte of the system cn be obtined by investigtion of prmeters of prticles floting in the hydrulic liquid 1. The mesurement of prticle concentrtion is the crucil prt of such monitoring becuse incresing numbers of prticles with prticulr sizes should men tht some prt of hydrulic system does not work properly or is ner to brek down. In spite of the fct tht severl utomtic prticle counters exist, they hve significnt limittion for the precise mesurement of reltively low concentrtion of prticle in cse of utilizing it inside of erospce systems or they re unble to mesure highest concentrtion in industril ones 5. Both issues cn be ddressed by implementtion of the CMOS imge sensor insted of single photodiode used in the most of modern APC. Firstly, the ccurcy of the prticle concentrtion mesurement is influenced by the ccurcy of mesurement of the volume of liquid to be investigted. Usully, the velocity of the prticle is used for determintion of the flow rte nd the time of nlysis wheres the volume is fixed (100 ml). The velocity of the prticle is mesured by APC using the durtion of the electric pulse t the output of the photodiode. * kornilin@ssu.ru; phone ; ssu.ru

3 However, the velocity of the prticle vries throughout the tube s in the centre we hve got the mximum speed compred to the lower one ner to the pipe wll. This issue cnnot be resolved by using photodiode s it cnnot mesures the position of the prticle inside of the tube. Generlly, the ssumption tht the verge speed is mesured by ech prticle gives sufficient results for high concentrtions. Nevertheless, in cse of pure systems like erospce the error of prticle concentrtion estimtion cnnot be lower thn 30 per cent or might be higher 6. In cse of using mtrix imge sensor the position of the prticle in the tube cn be determined by imge nlysis 7 nd the rel velocity cn be clculted. In our study we represent the method nd results of prticle concentrtion determintion bsed on ssumption tht the distribution of prticle velocity is prbolic throughout the chnnel. Clcultions bsed on the proposed lgorithm show tht the totl error in concentrtion estimtion is not exceed 10 per cent nd does not depend on liquid viscosity nd temperture. Secondly, the errors of prticle concentrtion estimtion re cused by mtches of different prticles inside of mesurement volume 6. The photodiode mesures severl prticles inside of mesurement volume s one. Typiclly, the restriction of the mximum mesured concentrtion is estblished for APC bsed on photodiodes. It is bout 1500 prticles per cm 3, which is not sufficient for the industril hydrulic systems. We proposed the lgorithm of estimtion of the ccurcy of the APC bsed on mtrix sensor. Clcultions mde by using Poisson distribution prove tht the improvement of the resolution (or the limit of concentrtion to be mesured) cn chieve in verge 0 times more compred to the APC with single photodiode.. MATERIALS AND METHODS The generl eqution to determine prticle concentrtion n is following : N n =, (1) V Where N stnds for the number of prticles inside of fixed volume of liquid V. This volume ccording to the regultion documents should be 100 ml. Therefore, we need to count N prticles during the period of time t while this fixed volume of liquid goes throughout the sensor. The period of time for liquid nlysis t depends on the flow rte inside of the sensor Q ccording to the formul : t а V =, () Q Generlly, the flow rte depends on the type of liquid nd vried from nlysis to nlysis. Therefore, the sensor should determine Q utomticlly. Q depends lso on the velocity of the liquid inside of sensor smple tube. The distribution of the velocities is shown in Figure 1..1 Time of nlysis for utomtic prticle counter bsed on photodiode Usully, the flow rte in in-line photodiode sensors is estimted by the verge velocity of liquid v vg in the sensor smple tube using following reltion 8 : Q = h v, (3) 4 χ vg where χ represents the size of the chnnel long with y xis divided by the size of chnnel long with x xis, h denotes the hlf of the chnnel size long with x xis. The verge velocity v vg is determined theoreticlly using eqution 8 : p h π χ 1 3 π χ vvg = ( th + th +...) µ l 3 π χ 3, (4) where p stnds for pressure difference on the smple tube, l denotes the width of diphrgm 6, 7 ; µ is kinemtic viscosity of the liquid.

4 Utilizing eqution (4) for determintion of v vg cses problems becuse of compliction in mesurement of p nd µ during the time of nlysis. Figure 1. The distribution of velocities inside of the sensor smple tube. The distribution ws clculted for the dimension of the smple tube section with sizes 700 µm long with x xis nd 1000 µm long with y xis. This mesurement lso requires some dditionl nd very specific instruments. Thus, the v vg is estimted by prticle velocity v vg in the chnnel which cn be mesured by the pulse durtion t the output of the photodiode 6 : where d denotes prticle size nd τ stnds for the pulse durtion. v vg l + d ' =, (5) τ However, mesurement ccording reltion (5) cuses dditionl error becuse v vg reltes to the instntneous speed of liquid v inside of smple tube nd this speed vries significntly in the slice of the tube. This instntneous speed v cn be clculted using following eqution in cse of lminr flow 8 : n + 1 π x n ch( ) 16 χ h p ( 1) χ h n + 1 π y v = 1 cos( ) 3, (6) 3 π µ l 1 n 0 ( n 1) n π = + + ch( ) χ h χ This velocity is shown in Figure 1. Eventully, time of the nlysis mesured by utomtic prticle counter bsed on photodiode is determined utilizing reltion: t а = V 4 χ h v, (7) where v v vg '.. Time of nlysis for utomtic prticle counter bsed on CMOS imge sensor In cse of using mtrix CMOS imge sensor we hve dditionl informtion bout coordinte of prticle flown inside of the smple tube. This coordinte cn be used for proper determintion of the verge velocity of the liquid inside of the tube. Combining reltion (3) nd (4), we lso getting the p from eqution (6), we cn clculte the time of nlysis s following:

5 t а 64 χ V = h v n + 1 π x n ch( ) ( 1) χ h n + 1 π y 1 cos( ) n + n + 1 π ch( ) χ h χ, (8) ( ) 3 π χ 3 3 n= 0 ( 1) 3 π π χ 1 3 π χ th th 5 3 This eqution is more suitble for mtrix CMOS imge sensor becuse it might be possible to determine x nd y coordintes of prticle trck nd mke some correction for known velocities distribution ccording to the (6). We lso need to know the chnnel size h tht is constnt nd cn be mesured. The velocity of the liquid cn be mesured by the velocity of the prticle inside of smple tube utilizing this reltion: v N t p z =, (9) exp where N z stnds for the size of prticle trck on the imge in number of pixels [Sn Diego], p is pixel size nd t exp denotes exposure time of CMOS imge sensor. Let F(x, y, χ) stnds for the lst prt of eqution (8) nd m for the first one. Then F(x, y, χ) reflects the velocity distribution inside the chnnel nd m represents the sizes of chnnel. Thus from (8) nd (9) we get the following: t а m texp = V F( x, y, χ), (10) N p z Eventully, we need to know the sizes of chnnel m, exposure time of CMOS sensor, the size of prticle trck nd pixel size in order to estimte the time of nlysis for the predefined volume V..3 Accurcy of estimtion of prticle concentrtion In ccordnce with (1), the bsolute error of prticle concentrtion mesurement is determined by the error of indirect mesurement: N 1 n = V N + V V, (11) Therefore, we need to determine the bsolute error of mesurement of volume V nd bsolute error of mesurement of the prticle number counting N..4 Accurcy of volume mesurement If we propose tht the flow rte is constnt vlue, we cn obtin the V from eqution (): V = Q t, (1) As follows from the equtions (1) nd (), the reltive error of volume determintion is equl to the reltive error of mesurement of nlysis time: V t t = =, (13) V V / Q t The bsolute error of nlysis time determintion for CMOS imge sensor consists of the errors of mesurement prticle velocities v y, v x nd error in mesuring prticle trck coordinte x, y:

6 t t t t y x v y v x x y t = v + v + x + y, (14) where t should be clculted ccording to the eqution (10). The bsolute error of prticle velocity mesurement is clculted utilizing formul (9) s following: p v = N z, (15) t exp where N z stnds for the bsolute error of prticle trck mesurement. The mximum vlue of N z is two pixels becuse when prticle trck consists of only two pixels, the true length of trck cn be less thn one pixel nd up to two pixels. In ddition, the totl influence of the error in mesuring prticle trck coordinte x, y re significntly lower thn errors of mesurement prticle velocities v y, v x becuse there re ten times more pixels long with mesurement volume thn in prticle trck. Therefore, the eqution (14) cn be rewritten s following: t p p = + t vy t э vx tэ, (16) Using reltion (9) nd propose the equl velocities long with both xes, eqution (16) cn be rewritten s following:.5 Accurcy of prticle counting t =, (17) t N z The bsolute error of counting prticles N in volume is cused by the prticle mtches inside of mesurement volume. Three cses re possible for prticle mtches shown in Figure. ) b) c) Figure. Different cses of mtches prticles inside of mesurement volume. In this cses severl prticles re not distinguished from the one prticle. Cse ) represents sitution when two prticles cn be counted s one by one pixel, cse b) shows the sitution of mtches severl prticles bove severl pixels nd c) reflects the cse when prticles projections re crossing The probbility of prticle mtches P err mens tht two or more prticles re in the predetermined volume. Let V eq stnds for such volume. P err cn be clculted on the bsis of the Poisson lw. The Poisson lw estimtes the probbility P m of prticle numbers presence inside of volume V 9 : P m m = e, (18) m! where m denotes the number of prticles, stnds for the verge number of prticle in the volume V. should be clculted s following 9 :

7 Thus, P err cn be clculted s following: = nv, (19) P = 1 P P, (0) err 0 1 where P 0 nd P 1 stnds for the probbility of bsence of ny prticle nd presence only one prticle in the volume respectively. Using reltions (0) nd (18) we cn obtin for the P err following eqution: 0 1 nv P eq err = e e = e e = e (1 + nveq ), (1) 0! 1! Therefore, P err should depend on V eq in cse of constnt concentrtion n. The estimtion of the volume is bsed on drwing in Figure 3. As the CMOS sensor is flt, the V eq cn be clculted s product of the chnnel width h nd the re on the surfce of the mtrix S eq. We cn consider two-dimensionl cse. S eq is presented in Figure 3. Figure 3. Determintion of the equivlent re S eq on the surfce of the mtrix CMOS imge sensor. d stnds for prticle dimeter, x eq is the side of S eq, d dd denotes dditionl intervl for prticles to be differentited by imge processing. As follows from Figure 3, the side of the S eq cn be clculted utilizing this eqution: Therefore, the V eq should be determined s following: x = ( d + d ), () eq dd V h S h d d By substitution of reltion (3) in (1) we obtin the eqution for P err : eq = eq = 4 ( + dd ), (3) n 4 h ( d + d dd ) dd P = 1 e (1 + n 4 h ( d + d ) ), (4) err 3.1 Accurcy of volume nd nlysis time mesurement 3. RESULTS AND DUSCUSSION Generlly, if we hve the fixed volume of liquid to be investigted nd fixed flow rte we should get the constnt time of nlysis s follows from the reltion (). However, this time depends on the method of the flow rte determintion s ws shown in the methods section. The result of clcultion of the time of nlysis in cse of using single photodiode utilizing eqution (7) is shown in Figure 4. As follows from the Figure 4, t vries significntly from the vlue of roughly 45 seconds in centre of chnnel up to uncertin vlue ner to the tube wll. Theoreticlly, if the prticle goes through the chnnel on the wll, the error cn be

8 infinite. The prticle counter cn be reclibrted to determine the mximum velocity in the centre of tube though. Consequently, it leds to less error especilly when the most of the prticle goes through the centre. However, the error is still depends on the coordinte of the prticle nd cn be significnt when the totl number of prticle in the volume V less thn 100. Figure 4. The time of nlysis in reltion with prticle coordinte inside of smple tube. The true vlue of time of nlysis is 75 seconds. The line denotes the true vlue of t, the dotted line is the t, determined by single photodiode sensor. In cse of using single photodiode the reltive error of volume determintion cn be clculted ccording to the reltion (13) nd (7). We cn lso obtin the reltive ccurcy of volume mesurement δv in reltion with the prticle coordinte. This error cn esily rech the vlue of 100 per cent nd more for prticles flown ner to the wll of the tube. Utilizing equtions (17) nd (13) we cn show the reltion between reltive error of volume mesurement nd the size of prticle trck 7 shown in Figure 5. Figure 5. The influence of the length of prticle trck on the reltive error of volume mesurement. Pixel size is 6 µm. According to Figure 5 the length of trck should not be less thn 0 pixels in order to chieve the ccurcy 90 per cent. Comprison of the results represented in Figures 4 nd 5 shows tht the implementtion of CMOS imge mtrix sensor reduces the error of volume mesurement down to 10 per cent, wheres sensor bsed on single photodiode hs significnt error up to infinite vlue.

9 Figure 6. The reltive error of volume mesurement in reltion of the prticle coordinte for single photodiode sensor (line), one CMOS imge sensor (dotted line) nd two CMOS imge sensors (dshed line). However, this error decrese is possible in cse of utilizing two mtrix sensors long with the x nd y xes of the smple tube. In prctice, only one mtrix cn be esily integrted inside of smple tube nd potentil error reduction is not complete. Figure 6 represents the reltive error of volume mesurement in reltion of the prticle coordinte for single photodiode sensor, one CMOS imge sensor nd two CMOS imge sensors. In cse of using two mtrix sensors the error does not depend on the prticle trck coordinte becuse both coordinte re determined nd the mesurement volume is corrected. Sensor with only one mtrix sensor hs lower error ner to the centre of chnnel becuse of only one mesurement error relted to only one mtrix. However, the error in this cse lso depends on the prticle trck coordinte. The error of the sensor with single photodiode three times higher s the velocity of prticle determintion is not s effective s in mtrix sensor. 3. Accurcy of prticle counting As reveled by formul (4), the error in prticle counting cused by prticle mtches depend on the size of sensor chnnel, the prticle concentrtion nd sizes. Let us choose the intervl of d dd equl to the size of pixel. The results of clcultion for prticle sizes of µm nd 00 µm re represented in Figure 7. Figure 7. The probbility of error in prticle counting cused by prticle mtches in dependence of prticle concentrtion. The error for prticle sizes µm shown by dotted line nd for 00 µm represented by line.

10 As cn be seen in Figure 7, the mximum concentrtion to be mesured for µm prticles significntly higher compred to the 00 µm prticles. If we set up the probbility of error on the level of 10 per cent, the mximum concentrtion will be pproximtely 10 1 prticles in m 3, wheres for 00 µm prticles it will be roughly The resolution of sensors bsed on CMOS mtrix sensor is more thn of single photodiode sensors. This fct is lso represented in Figure 8. Figure 8. Comprison of the probbility of error in prticle counting cused by prticle mtches in dependence of prticle concentrtion for single photodiode sensor (dotted line) nd CMOS imge sensor (line). Pixel size is 6 µm, the photodiode diphrgm is 140 µm x 700 µm. As reveled in Figure 8, the resolution of CMOS imge sensor is t lest 1000 times higher thn resolution of single photodiode sensor. This fct cn be predictble by comprison of the size of pixel 6 µm nd the size of sensitive re in single photodiode sensor with dimensions 140 µm x 700 µm. In ddition, we lso should consider the length of prticle trck in cse of using CMOS imge sensor, therefore the resolution will be t lest 100 times more thn in single photodiode sensor. 4. CONCLUSION This rticle provides the theoreticl bsis nd some results for the estimtion of the mximum concentrtion to be mesured by inline utomtic prticle counter bsed on CMOS imge sensor. The comprisons mde shows tht this sensor hs significnt benefits thn single photodiode sensors. In methods section presented the lgorithm of reducing error cused by the different prticle velocities inside of mesuring chnnel of the sensor to be implemented in CMOS imge sensors. The method of choosing proper prmeters of CMOS imge prticle sensor like pixel size, exposure time is lso provided. The mterils in this rticle cn lso be used for the ccurcy estimtion for both single photodiode nd CMOS imge prticle sensors. REFERENCES [1] Fitch, E. C., [Fluid Contnintion Control], Technology trnsfer Series 4, Oklhome, 15-3 (1988). [] Logvinov, L. M., [The Dignostics of Fluid Systems of Equipment Using the Prmeters of the Hydrulic Fluid], CNTI Poisk, Moscow, 5-0 (199). [3] Fitch, J., "The Usefulness of Prticle Counting in Oil Anlysis, " EPRI/NMAC Lube Notes 1, 5-5 (00) [4] Fitch, J., "In-line Contmintion Mesurement Device, " U.S. Ptent No , 1-10 (1994). [5] Kornilin, D. V., Kudryvtsev, I. A., Voronof, A. F. et l, "Defining the prmeters of the disperse phse sensor built-in control of hydrulic systems bsed on CMOS-mtrix," Devices 5, (010). [6] Kudryvtsev, I. A. [Incresing the Resolution nd Sensitivity of the Built-in Control of the Dispersed Phse of Photoelectric Converters for Control Systems], SSAU, Smr, (1999).

11 [7] Kornilin, D. V., Kudryvtsev, I. A., McMill A. J. et l, Determintion of prticle sizes in hydrulic liquids bsed on imge- nd subpixel processing, Proc. SPIE 9971, (016). [8] Loytsynskiy, L. G., [Mechnics of liquids nd gses], Nuk, Moscow, (1973). [9] Ventsel, E.S., [The theory of probbility], Vyshy shkol, Moscow, (1998).